Calculus Examples

$\int 5 (5 x + 7) d x$

Step 1

Multiply $5 (5 x + 7)$ .

$\int 5 (5 x) + 5 \cdot 7 d x$

Step 2

Simplify.

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Step 2.1

Multiply $5$ by $5$ .

$\int 25 x + 5 \cdot 7 d x$

Step 2.2

Multiply $5$ by $7$ .

$\int 25 x + 35 d x$

Step 3

Split the single integral into multiple integrals.

$\int 25 x d x + \int 35 d x$

Step 4

Since $25$ is constant with respect to $x$ , move $25$ out of the integral.

$25 \int x d x + \int 35 d x$

Step 5

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$25 (\frac{1}{2} x^{2} + C) + \int 35 d x$

Step 6

Apply the constant rule.

$25 (\frac{1}{2} x^{2} + C) + 35 x + C$

Step 7

Simplify.

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Step 7.1

Combine $\frac{1}{2}$ and $x^{2}$ .

$25 (\frac{x^{2}}{2} + C) + 35 x + C$

Step 7.2

Simplify.

$\frac{25 x^{2}}{2} + 35 x + C$

Step 7.3

Reorder terms.

$\frac{25}{2} x^{2} + 35 x + C$